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Bootstrap estimation of actual significance levels for tests based on estimated nuisance parameters

Yao, Qiwei, Yang, Wengyan and Tong, Howell (2001) Bootstrap estimation of actual significance levels for tests based on estimated nuisance parameters. Statistics and Computing, 11 (4). pp. 367-371. ISSN 0960-3174

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Abstract

Often for a non-regular parametric hypothesis, a tractable test statistic involves a nuisance parameter. A common practice is to replace the unknown nuisance parameter by its estimator. The validality of such a replacement can only be justified for an infinite sample in the sense that under appropriate conditions the asymptotic distribution of the statistic under the null hypothesis is unchanged when the nuisance parameter is replaced by its estimator (Crowder M.J. 1990. Biometrika 77: 499–506). We propose a bootstrap method to calibrate the error incurred in the significance level, for finite samples, due to the replacement. Further, we have proved that the bootstrap method provides a more accurate estimator for the unknown actual significance level than the nominal level. Simulations demonstrate the proposed methodology.

Item Type: Article
Official URL: http://www.springer.com/statistics/computational/j...
Additional Information: © 2001 Springer Verlag
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Collections > Economists Online
Departments > Economics
Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Funders: Biotechnology and Biological Sciences Research Council, Engineering and Physical Sciences Research Council
Date Deposited: 30 Jun 2008 11:05
URL: http://eprints.lse.ac.uk/6103/

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